1. Field of the Invention
The present invention relates to quantum information processing, and, in particular, to techniques for reducing the complexity of quantum processing on quantum bits (qubits) represented by quantum states of single photons and to techniques for using nanocavities to enhance nonlinear effects including two-photon absorption.
2. Description of the Related Art
Information processing using classical computers relies on physical phenomena, such as magnetic fields, voltages, and optical intensity that can be produced and measured in each of two basis states, one basis state representing a zero and another basis state representing a one. Each physical element that can achieve either of these two states represents one binary digit, called a bit. Quantum information processing uses physical elements that exhibit quantum properties that may include, not only one of the two or more basis states, but also an arbitrary superposition state of the basis states. A superposition state has some non-zero probability of being measured as one of the basis states and some non-zero probability of being measured as another of the basis states. A physical element that exhibits quantum properties for two basis states represents one quantum bit, also called a qubit. Physical elements that are suitable for representing qubits include the spins of single electrons, electron states in atoms or molecules, nuclear spins in molecules and solids, magnetic flux, spatial propagation modes of single photons, and polarizations of single photons, among others.
Logical operations performed on qubits apply not only to the basis states of those qubits but also to the superposition states of those qubits, simultaneously. Quantum computers based on logical operations on systems of qubits offer the promise of massively simultaneous processing (also called massively parallel processing) that can address problems that are considered intractable with classical information processing. Such classically intractable problems that can be addressed with quantum computers include simulation of quantum interactions, combinatorial searches of unsorted data, finding prime factors of large integers, solving for cryptographic keys used in current secure communication algorithms, and truly secure communications (also called “quantum cryptography”).
Several approaches use single photons to represent qubits. In many respects, single photons are advantageous for serving as qubits in a quantum computer. Photons can be easily generated and manipulated. Optical fibers can be used to make connections in analogy with the wires of a conventional computer; while most other phenomena representing qubits interact only with nearest neighbors. Photons interact only weakly with the environment because photons have no charge and no rest mass. The main difficulty in an optical approach has been the implementation of quantum logic gates due to the weak interaction between individual photons.
One approach uses linear interactions between single photons but relies on interferometer techniques, e.g., interference on two spatial modes of propagation for a single photon. These devices are called “probabilistic” logical gates because they perform the desired logical operation in response to only a fraction of the input photons. However, it can be determined when an operation is performed successfully, so that, in a separate step often called a “post selection” step or a “post-detection selection” step, output photons are blocked unless the operation is successfully performed. It has been shown that the fraction can be increased close to a value of one with sufficient numbers of components and extra photons (called “ancilla photons” or “ancilla”) in particular states.
While suitable for many purposes, logical gates based on this approach suffer thermally induced phase shifts between photons taking different paths. In addition, this approach suffers from complexity introduced to generate and manipulate a large number of ancilla. Also, such approaches are subject to errors in the detectors used to detect ancilla photons during the post selection step.
In a more recent approach, logical devices that operate on the polarization states of single photons have been proposed that do not suffer thermally induced phase shifts and that do not require as large a number of ancilla and additional components and resources. This approach is described, for example, in U.S. patent application Ser. No. 10/286,735, filed 1 Nov. 2002, entitled “Techniques for Performing Logic Operations Using Quantum States of Single Photons,” by Todd B. Pittman, James D. Franson and Bryan C. Jacobs (hereinafter referenced as “Pittman”).
In another recent approach, the number of ancilla is decreased by proper generation of an entangled state for the ancilla selected to reduce errors. This approach is described, for example, in U.S. patent application Ser. No. 10/651,317, filed 28 Aug. 2003, entitled “Techniques For High Fidelity Quantum Teleportation And Computing,” by James D. Franson, Michelle Donegan, Michael Fitch, Bryan C. Jacobs and Todd B. Pittman, (hereinafter referenced as “Franson”).
While representing advances over prior techniques, the recent approaches still sometimes use a large number of ancilla and therefore suffer to some degree from the complexity introduced to generate and manipulate those ancilla. Also, these recent approaches are sometimes also subject to errors in the detectors used to detect the ancilla photons during a post selection step.
Based on the foregoing description, there is a clear need for techniques that reduce the complexity of quantum logic operations on qubits represented by single photons, which techniques do not suffer the deficiencies of current approaches. In particular, there is a clear need for techniques that reduce the reliance on ancilla while performing quantum information processing. Furthermore, techniques for enhancing any new approach are also needed.
The approaches described in this section could be pursued, but are not necessarily approaches that have been previously conceived or pursued. Therefore, unless otherwise indicated herein, the approaches described in this section are not to be considered prior art to the claims in this application merely due to the presence of these approaches in this background section.